Greetings from Canada. Although we don’t have children- here are my thoughts:

In Dublin - there is a zoo in Phoenix Park. Had we had more time I would have loved to seen it.

An hour outside of Dublin is New Grange. It’s neat to see and travel inside the structure which is like walking into a cave with some sections you can only squeeze through the stones sideways.

Belfast is around 2 hrs approx north of New Grange - really neat to see and there is a CS Lewis parkette with statutes from Lion Witch & The Wardrobe. The city tour in Belfast is also truly fascinating. You could all write on “the wall”.

From Belfast you are super close to the Rope Bridge, Giants Causeway, Dunluce Castle and dark hedges (game of thornes). These can all be done in one days as they are all about 15 minutes apart from each other. I think these would be interesting for children..,, maybe not the hedges.

In the other direction - if you decide to go to the Cliffs of Mohar then a must see are the Doolin caves - that would be truly interesting for young children.